One aspect of my style in chess is that I like to trade a lot.
Is trading too much bad?
Trading for the sake of trading is bound to be in your opponent's favour more often than not.
Generally speaking, recapturing often activates the piece that can capture back. Consider two rooks on an open file, both protected by another, pretty passive rook on the a-file. The side that trades loses control of the open file and is stuck with the a-file rook, but the sides that recaptures gets to move his previously passive rook from the a-file to the open file.
Also, if you delay trading, you keep options open. As long as you still have several options, the opponent has to keep defences up against all of them, but as soon as you actually choose one (make the trade), that releases tension and usually frees up the game of the opponent a bit. Don't release tension without a reason.
Worst, if the opponent knows that you like to trade, he may offer trades that work in his favour positionally, and you'll go for them. That will get you a bad position very quickly.
A trade is a way to change the nature of the position. Only go for trades that change the position in your favour, otherwise keeping the opponent guessing is better.
Trading pieces off the board being good or bad usually depends on the position, and there are a variety of situations to consider that could lead to a positional advantage.
1) Try to avoid trades when behind in material. If your behind 3 points in material, the more pieces that come off the board, the more crippling that disadvantage comes. The more pieces on the board, the more you have to work with to create discovered attacks, forks, skewers, pins etc. On the flip side, try to force trades when your ahead in material, as the more pieces comes off the board, the more you will disarm your opponents ability to fight back.
The image above is from one of my games that I'm currently playing online in correspondence with myself as the white pieces. Here I've just captured a pawn with my last queen move. My goal is to pick off as many pawns as I can, and if an opportunity to force the trading of the queens and rooks comes off the table comes I will take it. Being up an entire rook is a big advantage, in an end game position where black has no rook or queen, white can easily use his rook and king to pick off pawns for an easy end game win.
2) It's always a great idea to trade off a bad minor piece for your oponents good pieces. For example, consider this board:
In this position black has what's considered to be a bad light squared bishop, the reason being the pawns. All of blacks pawns are locked in on light squares, getting in the way of the black bishop. Where as whites bishop is very very good, because it has plenty of targets to go after and capture. Together with careful maneuvering of both players kings white has better chances to win this end game. So trading the bishops off for the white player is a bad decision, where as if the bishops could come off the board, it would be better for black.
3) Closed versus open games
In general when you have a closed game, knights are better than bishops. And bishops are usually better on an open game. The pawns will dictate whether the board is open or closed. If the pawns are set up in a way that closes down the diagonals, disallowing the bishops from slicing through the board, then it's closed. If you can capture a knight with a bishop in a closed game, that will usually help your position. The image below is an example of an open game.
4) Monster Piece
It's a very good idea to trade off a piece that is dominating your position. Take this example where white has it's knight firmly placed in the d5 square.
This knight can comfortably attack the majority of the board for the black army. If black can remove such a threat by trading off his own knight, it would improve the situation for him.
5) Cramped Positions
If your army is hemmed in by your own pawns, preventing the natural development of your pieces towards the center of the board then it's a great idea to trade off pieces to give your pieces more options to attack and defend.
Looking at the image above, we can see that black is experiencing a cramped position to the extreme! Only blacks queen and knight has some options for movement, where as if you look at white's game it's much easier to play. White's bishop can slice through the position and attack key defending pawns, the white knight can jump in at all any time, both rooks are connected and could easily be swung over to the A1 file to apply even more pressure. White should keep the tension, where as black should to try to trade and release the pressure.
Those are some of the major themes and ideas that I follow in my own games. Of course there is always exceptions and the position of the pawns generally drive which decisions are good and bad.
I hope this helps!
Basically you want to trade from a position of strength. If you have, say, a pawn advantage, you will want to trade piece.
Another time to trade is when you have positional advantage. What you do is to keep build the advantage and keep pressure on the opponent. To relieve the pressure, your opponent will offer trades. Then you should trade, but only on your terms, e.g. where your recaptures keep the pressure on, or where you have a good knight against a bad bishop, or the bishop pair against a bishop and knight.
On the other hand, you don't want to trade when your opponent is ahead in material, or his recapture will place one of his pieces in a dominant position. In that case, keep more pieces on the board, and hope to find "salvation in complexity."
Besides the pure chess reasoning others have given,
One other thing is player strength at different phase of the game. If you are good at endgame and you know you opponent isn't, then you would benefit from a simplified position.
Also to consider is clock. If opponent is under time pressure, don't trade. Keep the game complex and wait for a blunder.